1. Field of the invention
The present invention relates to the synthesis of high frequency signals and, in particular, discloses a method and system for synthesizing high frequency audio signals.
2. Background of the Invention
The digital recording of audio signals has become extremely popular. The most popular format for recording is the CD audio format which samples a signal at approximately 44.1 KHz. This is likely to produce a corresponding audio range of approximately 20 kHz which was thought to be adequate for reproducing the audio range that the human ear can detect. However, it is thought by some that the human ear is able to colour an audio signal through the utilization of portions of a signal above 20 kHz. Hence, recent standards have proposed either an 88.2 or a 96 kHz sampling rate. There is therefore the significant problem of how one takes, for example, a 44.1 kHz recorded signal and remasters the signal in say an 88.2 kHz format. One standard technique utilized is to use an interpolator that also uses some kind of linear filter to perform an anti alias filtering operation.
For the purposes of further discussion, the following terminology is defined:                The original signal is called the Original Audio Signal.        The original audio sample rate is called the Original Sample Rate.        The original audio signal is believed to be “accurate” up to a frequency known as the Original Frequency Range.        The Original Half Nyquist Frequency is defined as 0.5 times the Original Sample Rate.        The interpolated signal is called the Interpolated Audio Signal.        The new (higher) audio sample rate is called the Interpolated Sample Rate.        The Interpolated Half Nyquist Frequency is defined as 0.5 times the Interpolated Sample Rate.        The Oversampling Ratio is the Interpolated Sample Rate divided by the Original Sample Rate.        
Typical values of the above defined quantities are
For a CD player with 4× oversampling D/A converters:                Original Sample Rate=44,100 Hz        Original Frequency Range=20,000 Hz        Original Half Nyquist Frequency=22,050 Hz        Interpolated Sample Rate=176, 400 Hz        Interpolated Half Nyquist Frequency=88, 200 Hz        
In a system like this, the Original Audio Signal only contains reliable content up to 20 kHz, but it is assumed it may be desirable to synthesize new high frequency content up to say 88.2 kHz.
For a DVD player with 2× oversampling D/A converters:
Original Sample Rate=48,000 Hz ′Original Frequency Range=20,000 Hz Original Half Nyquist Frequency=24,000 Hz
Interpolated Sample Rate=96,000 Hz Interpolated Half Nyquist Frequency=48,000 Hz
In a system like this, the Original Audio Signal only contains reliable content up to 20 kHz, but it may be desirable to synthesize new high frequency content up to 48 kHz.
The standard prior art anti-aliasing approach to higher sampling rate extension operates on the principle that as no information about what audio content may have existed above the Original Half Nyquist Frequency is provided in the original audio material, it is necessary to ensure that an Interpolated Audio Signal has zero content in this upper frequency range.
The standard prior art method for producing an interpolated signal will now be described. Turning initially to FIG. 1, an original audio signal 1 is provided having samples e. g., 11,12. The samples are assumed to have been provided at a standard rate. The first step in forming the interpolated signal is to zero pad the audio signal as illustrated in FIG. 2. In zero padding, zero value signals e. g., 14,15 are added to the signal between samples. Next, as illustrated in FIG. 3, an interpolation process is provided where the signal e. g., 18 is formed from an interpolation of the two signals 17,19. In the example provided, the interpolated sample rate is twice the original sample rate and hence the over sampling ratio is 2 with one zero sample inserted between each sample of the original audio signal. The zero-padding technique results in aliasing, meaning that the low frequency audio signal is duplicated in higher frequency bands. These higher frequency replicas (called aliases) are then filtered out (using a low-pass filter), to leave the Interpolated Audio Signal.
An example of aliasing is illustrated in FIG. 4 where an original audio signal having a frequency spectrum 21 is zero padded resulting in the zero padded audio signal having a frequency spectrum 23,24 with the lower frequency being replicated in high frequency bands. The interpolation process is equivalent to applying a low-pass filter 27 which results in the interpolated audio signal 29 which substantially reflects the original audio signal 21.
The arrangement of the prior art has a significant disadvantage in that none of the high frequency spectrum is utilized when a re-sampling occurs.